Electricity is commonly delivered from electricity suppliers to consumers in the form of alternating current (AC) at a certain fundamental frequency, e.g., 60 Hz in the U.S. The consumption of electricity, e.g., three-phase AC, is commonly measured by power meters. It is known that when the load of a power supply system includes non-linear components, the electrical power supply includes harmonic frequencies other than the fundamental frequency. Additionally, when the load is not purely resistive, the waveform of voltage V may lead or lag the waveform of current I in time or have a phase offset in the frequency domain.
Electrical power may include three components: apparent power (Papp), active power (Pact), and reactive power (Preact). The apparent power Papp is defined as the product of magnitudes of voltage V and current I, i.e., P=V×I. The active power Pact is defined as the capacity of the load at a particular time or the energy that flows from power source to the load. The reactive power Preactive is defined as the energy that is bounced back from the load to the source. If the phase offset between current and voltage in frequency is φ, then Pact=Papp*|cos(φ)| and Preact=Papp*|sin(φ)|.